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The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

Let G be a graph and S a subgraph of G. Let the number of odd components in G-S be denoted S^', and |S| the number of graph vertices of S. The condition |S|>=S^' for every ...

The tetranacci constant is ratio to which adjacent tetranacci numbers tend, and is given by T = (x^4-x^3-x^2-x-1)_2 (1) = 1.92756... (2) (OEIS A086088), where (P(x))_n ...

The tribonacci constant is ratio to which adjacent tribonacci numbers tend, and is given by t = (x^3-x^2-x-1)_1 (1) = 1/3(1+RadicalBox[{19, -, 3, {sqrt(, 33, )}}, ...

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...

The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area ...

Consider the process of taking a number, taking its digit sum, then adding the digits of numbers derived from it, etc., until the remaining number has only one digit. The ...